# Centered tetrahedral number

We are given integer n, we need to find n-th centered tetrahedral number.

Description: The centered tetrahedral number is a centered figurate number that represents a tetrahedron.

Tetrahedral Numbers: A number is termed as a tetrahedral number if it can be represented as a pyramid with a triangular base and three sides, called a tetrahedron. The nth tetrahedral number is the sum of the first n triangular numbers.
The first few centered tetrahedral number series are:
1, 5, 15, 35, 69, 121, 195, 295, 425, 589……………………….

Mathematical nth Term of centered tetrahedral number: Examples :

Input : n = 3
Output : 35

Input : n = 9
Output : 589


Below is the implementation of above formula.

## C++

 // C++ Program to find nth  // Centered tetrahedral number  #include  using namespace std;     // Function to find centered  // Centered tetrahedral number  int centeredTetrahedralNumber(int n)  {      // Formula to calculate nth      // Centered tetrahedral number      // and return it into main function.      return (2 * n + 1) * (n * n + n + 3) / 3;  }     // Driver Code  int main()  {      int n = 6;         cout << centeredTetrahedralNumber(n);         return 0;  }

## Java

 // Java Program to find nth Centered  // tetrahedral number  import java.io.*;     class GFG {         // Function to find centered      // Centered tetrahedral number      static int centeredTetrahedralNumber(int n)      {                     // Formula to calculate nth          // Centered tetrahedral number          // and return it into main function.          return (2 * n + 1) * (n * n + n + 3) / 3;      }             // Driver Code            public static void main (String[] args)      {          int n = 6;             System.out.println(                     centeredTetrahedralNumber(n));      }  }     // This code is contributed by anuj_67.

## Python3

 # Python program to find nth   # Centered tetrahedral number     # Function to calculate  # Centered tetrahedral number     def centeredTetrahedralNumber(n):         # Formula to calculate nth      # Centered tetrahedral number      # and return it into main function             return (2 * n + 1) * (n * n + n + 3) // 3    # Driver Code  n = 6 print(centeredTetrahedralNumber(n))                         # This code is contributed by ajit

## C#

 // C# Program to find nth Centered  // tetrahedral number  using System;     class GFG {         // Function to find centered      // Centered tetrahedral number      static int centeredTetrahedralNumber(int n)      {                     // Formula to calculate nth          // Centered tetrahedral number          // and return it into main function.          return (2 * n + 1) * (n * n + n + 3) / 3;      }             // Driver Code            public static void Main ()      {          int n = 6;             Console.WriteLine(                  centeredTetrahedralNumber(n));      }  }     // This code is contributed by anuj_67.

## PHP

 

Output :

195


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